Enhanced nonlinear response of fractal clusters

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Abstract
The enhanced linear and nonlinear response due to clustering of a nonlinear material in a host medium is studied in a regular fractal model and in the nonlinear differential effective-medium approximation (DEMA). The results show that a large enhancement in the nonlinear response is found for the case of a nonlinear fractal embedded in a linear host of the better conductor. We further investigate the conductivity-ratio dependence of the linear and nonlinear response. It is shown that by choosing a relevant scaling variable properly, the nonlinear response function can be rescaled to collapse onto a universal curve. The DEMA results are compared with the fractal results and excellent agreement is found. Physical consequences and implications of the results are discussed.